Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes.

In this paper we investigate the following two questions: Q1: Do there exist optimal proof systems for a given language L? Q2: Do there exist complete problems for a given promise class C? For concrete languages L (such as TAUT or SAT) and concrete promise classes C (such as NP∩coNP, UP, BPP, disjoint NP-pairs etc.), these ques-tions have been intensively studied during the last years, and a number of characterizations have been obtained. Here we provide new character-izations for Q1 and Q2 that apply to almost all promise classes C and languages L, thus creating a unifying framework for the study of these practically relevant questions. While questions Q1 and Q2 are left open by our results, we show that they receive affirmative answers when a small amount on advice is avail-able in the underlying machine model. This continues a recent line of research on proof systems with advice started by Cook and Kraj́ıček [6]

Cubic anisotropy in high homogeneity thin (Ga,Mn)As layers

Historically, comprehensive studies of dilute ferromagnetic semiconductors, e.g., $p$-type (Cd,Mn)Te and (Ga,Mn)As, paved the way for a quantitative theoretical description of effects associated with spin-orbit interactions in solids, such as crystalline magnetic anisotropy. In particular, the theory was successful in explaining {\em uniaxial} magnetic anisotropies associated with biaxial strain and non-random formation of magnetic dimers in epitaxial (Ga,Mn)As layers. However, the situation appears much less settled in the case of the {\em cubic} term: the theory predicts switchings of the easy axis between in-plane $\langle 100\rangle$ and $\langle 110\rangle$ directions as a function of the hole concentration, whereas only the $\langle 100\rangle$ orientation has been found experimentally. Here, we report on the observation of such switchings by magnetization and ferromagnetic resonance studies on a series of high-crystalline quality (Ga,Mn)As films. We describe our findings by the mean-field $p$-$d$ Zener model augmented with three new ingredients. The first one is a scattering broadening of the hole density of states, which reduces significantly the amplitude of the alternating carrier-induced contribution. This opens the way for the two other ingredients, namely the so-far disregarded single-ion magnetic anisotropy and disorder-driven non-uniformities of the carrier density, both favoring the $\langle 100\rangle$ direction of the apparent easy axis. However, according to our results, when the disorder gets reduced a switching to the $\langle 110\rangle$ orientation is possible in a certain temperature and hole concentration range.Comment: 12 pages, 9 figure

Novel Quaternary Dilute Magnetic Semiconductor (Ga,Mn)(Bi,As): Magnetic and Magneto-Transport Investigations

Magnetic and magneto-transport properties of thin layers of the (Ga,Mn)(Bi,As) quaternary dilute magnetic semiconductor grown by the low-temperature molecular-beam epitaxy technique on GaAs substrates have been investigated. Ferromagnetic Curie temperature and magneto-crystalline anisotropy of the layers have been examined by using magneto-optical Kerr effect magnetometry and low-temperature magneto-transport measurements. Postgrowth annealing treatment has been shown to enhance the hole concentration and Curie temperature in the layers. Significant increase in the magnitude of magnetotransport effects caused by incorporation of a small amount of Bi into the (Ga,Mn)As layers revealed in the planar Hall effect (PHE) measurements, is interpreted as a result of enhanced spin-orbit coupling in the (Ga,Mn)(Bi,As) layers. Two-state behaviour of the planar Hall resistance at zero magnetic field provides its usefulness for applications in nonvolatile memory devices.Comment: 10 pages, 3 figures, to be published in the Proceedings of ICSM-2016 conferenc

Post-growth annealing of GaMnAs under As capping - an alternative way to increase Tc

We demonstrate that in situ post-growth annealing of GaMnAs layers under As capping is adequate for achieving high Curie temperatures (Tc) in a similar way as ex situ annealing in air or in N2 atmosphere practiced earlier.Comment: 13 pages, 4 figure

Spatially controlled formation of superparamagnetic (Mn,Ga)As nanocrystals in high temperature annealed (Ga,Mn)As/GaAs superlattices

The annealing-induced formation of (Mn,Ga)As nanocrystals in (Ga,Mn)As/GaAs superlattices was studied by X-ray diffraction, transmission electron microscopy and magnetometry. The superlattice structures with 50 A thick (Ga,Mn)As layers separated by 25, 50 and 100 A thick GaAs spacers were grown by molecular beam epitaxy at low temperature (250 C), and then annealed at high temperatures of: 400, 560 and 630 C. The high temperature annealing causes decomposition to GaMnAs ternary alloy and formation of (Mn,Ga)As nanocrystals inside the GaAs matrix. The nanocrystals are confined in the planes that were formerly occupied by (Ga,Mn)As layers for up to the 560 C of annealing and diffuse throughout the GaAs spacer layers at 630 C annealing. The corresponding magnetization measurements show the evolution of the magnetic properties of as-grown and annealed samples from ferromagnetic, through superparamagnetic to the combination of both.Comment: 14 pages, 3 figure

Magnetodielectric effect and optic soft mode behaviour in quantum paraelectric EuTiO3 ceramics

Infrared reflectivity and time-domain terahertz transmission spectra of EuTiO3 ceramics revealed a polar optic phonon at 6 - 300K, whose softening is fully responsible for the recently observed quantum paraelectric behaviour. Even if our EuTiO3 ceramics show lower permittivity than the single crystal due to a reduced density and/or small amount of secondary pyrochlore Eu2Ti2O7 phase, we confirmed the magnetic field dependence of the permittivity, also slightly smaller than in single crystal. Attempt to reveal the soft phonon dependence at 1.8K on the magnetic field up to 13T remained below the accuracy of our infrared reflectivity experiment

Photoreflectance Study of the Fundamental Optical Properties of (Ga,Mn)As Epitaxial Films

Fundamental optical properties of thin films of (Ga,Mn)As diluted ferromagnetic semiconductor with a low (1%) and high (6%) Mn content and of a reference GaAs film, grown by low-temperature molecular-beam epitaxy, have been investigated by photoreflectance (PR) spectroscopy. In addition, the films were subjected to complementary characterization by means of superconducting quantum interference device (SQUID) magnetometry, Raman spectroscopy, and high resolution X-ray diffractometry. Thorough full-line-shape analysis of the PR spectra, which enabled determination of the E0 electronic transition in (Ga,Mn)As, revealed significant differences between the energy band structures in vicinity of the {\Gamma} point of the Brillouin zone for the two (Ga,Mn)As films. In view of the obtained experimental results the evolution of the valence band structure in (Ga,Mn)As with increasing Mn content is discussed, pointing to a merging the Mn-related impurity band with the host GaAs valence band for high Mn content.Comment: 21 pages, 6 figure

The deduction theorem for strong propositional proof systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs